Can I do a CA with a BCom from Narsee Monjee College of Commerce and Economics, Mumbai?

Definitely, you can do both CA as well as B.Com at the same time from Narsee Monjee College of Commerce and Economics, Mumbai. However, managing both at the same time will be difficult. 

The college has a very strict attendance policy of 75%. So basically you will need to attend classes every day. Living in a city like Mumbai, traveling to and fro to attend lectures, managing studies along with a job is not something that everyone can handle. Even if your attendance percentage is slightly lower than 75% the college will debar you from giving exams and may even expel you from the program. Some students even develop health issues due to such a rigorous schedule.

Now, these are the problems with doing CA and B.Com at the same time. But if you can handle the pressure, then definitely you should do it.